Question: You have $5$ reindeer, Balthazar, Jebediah, Lancer, Quentin, and Ezekiel, and you want to have $4$ fly your sleigh. You always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Explanation: We can build our line of reindeer one by one: there are $4$ slots, and we have $5$ different reindeer we can put in the first slot. Once we fill the first slot, we only have $4$ reindeer left, so we only have $4$ choices for the second slot. So far, there are $5 \cdot 4 = 20$ unique choices we can make. We can continue in this way for the third reindeer, and so on, until we reach the last slot, where we will have $2$ choices for the last reindeer. So, the total number of unique choices we could make to get to an arrangement of reindeer is $5\cdot4\cdot3\cdot2$. Another way of writing this is $\dfrac{5!}{(5-4)!} = 120$